@Article{CMR-39-2,
author = {Wang, Liang-Wei and Wang, Shu-Ying and Yin, Jingxue and Zheng-Wen, Tu},
title = {Complicated Asymptotic Behavior of Solutions for the Cauchy Problem of Doubly Nonlinear Diffusion Equation},
journal = {Communications in Mathematical Research },
year = {2023},
volume = {39},
number = {2},
pages = {231--253},
abstract = {<p style="text-align: justify;">In this paper, we analyze the large time behavior of nonnegative solutions to the doubly nonlinear diffusion equation $$u_t−{\rm div}(|∇u^m|^{p−2}∇u^m)=0$$ in $\mathbb{R}^N$ with $p&gt;1,$ $m&gt;0$ and $m(p−1)−1&gt;0.$ By using the finite propagation property and the $L^1-L^∞$ smoothing effect, we find that the complicated asymptotic behavior of the rescaled solutions $t^{\mu/2}u(t^{β_·},t)$ for $0&lt;\mu&lt;2N/(N[m(p−1)−1]+p)$ and $β&gt;(2−\mu[m(p−1)−1])/(2p)$ can take place.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2022-0050},
url = {https://global-sci.com/article/81458/complicated-asymptotic-behavior-of-solutions-for-the-cauchy-problem-of-doubly-nonlinear-diffusion-equation}
}